I'm working on a bottom end Falcon, bringing it back from being single speeded.
I just put a Shimano cartridge BB in it and the left and right threads on the BB shell must be miss-aligned. If I tighten down both sides of the BB, the BB becomes stiff. You can see the BB sits slightly crooked when the main body of the BB is installed. I had to loosen the main body to get the sliding side in.
If I tighten the sliding side tight the BB binds pretty hard. If I leave it slightly loose, it's not bad but still a bit of drag.
I'm sure the BB is not cross threaded as I was able to thread both sides in by hand.
It's not that it needs facing as the problem is there before the main body is tightened all the way down.
Having it chased won't change the alignment of the threads.
I don't see any way around it other than leaving the sliding cup slightly loose - after all, it just supports the body.

I'm thinking that if the length of engaged threading were shortened, that the flange seating forces might do a better job of keeping the cartridge centered along the centerline of the shell.

Does a standard fixed cup sit square with the face of the shell? If so, perhaps the length of engaged threading or the thread's tolerances would explain the difference.

Another solution might be a cartridge bb with some thousands of miles on it already, or a cartridge bb where tilting forces might allow the cartridges to self-align to some degree.

Maybe it will be a cup/cone bb that ends up giving the most satisfactory service, or one of those cartridge bb's for use on threadless shells or on shells with damaged threads.

The use of piloted taps is something else that I might look into.

If the shell is faced, go with a threadless unit and you'll be good.